Here's what Michael Behe says on page 39 of Darwin's Black Box.
By irreducibly complex I mean a single system composed of several well-matched, interacting parts tat contribute to the basic function, wherein the removal of any one of the parts causes the system to effectively cease functioning. An irreducibly complex system cannot be produced directly (that is by continuously improving the initial function, which continues to work by the same mechanism) by slight, successive modifications of a precursor system, because any precursor to an irreducibly complex system that is missing a part is by definition nonfunctional.Behe then goes on to say that an irreducibly complex system cannot evolve by natural selection.
The definition is not a problem. By this definition there are many irreducibly complex systems in biology. For example, the bacterial flagella is a pretty good example as long as you relax the criteria a little bit. (Some of the minor parts can easily be removed without affecting the overall function.)
The problem is not with the definition, it's with the conclusion. Irreducibly complex systems can easily evolve. All that's required is for the simpler intermediates to have some function other than the one seen in the final completed structure. In the case of the bacterial flagella this simpler function was secretion of large molecules. The flagella evolved from a type III secretion system by just adding a few extra components.
Thus, as Behe says above, it was not produced directly by continuously improving the initial function. Instead, there were several intermediate functions (e.g., secretion) that preceded the shift to the final function we observe today. This is how irreducibly complex systems evolve.
The citric acid cycle is another example of an irreducibly complex system for which there's an easily understood evolutionary pathway. The circular pathway arose when the ends of a forked pathway were joined by evolution of a single enzyme [Defining Irreducible Complexity].
Irreducible complexity is a concept invented by Intelligent Design Creationists. You'd think they would at least make the effort to understand something they created!